Converting to an alt and then back is an excellent way to mix bitcoins. Use an exchange, so that the sending wallet which sends out your bitcoins has a diferent address to the one you used to deposit the coins.
There's no need to do the alt bit if you're using an exchange. Send Bitcoin. Withdraw Bitcoin. It's pretty much guaranteed to come from a totally unrelated wallet to the one you sent it to. If you buy an alt in the middle bit you're just wasting fees and moving around the exchange's internal ledger.
That's not much use if the BTC you want to mix is involved in something against the exchange's terms and conditions like gambling but fine for straightforward breaking the link between old and new addresses for future privacy. You still don't want to be doing anything against their terms if you plan on using them again though.